In GHD, we assume that the system is initially in a fluctuating state which is, at every point in space, very well described by a state of Gibbs form, where entropy is maximised with respect to all available conservation laws. In integrable models these are the generalised Gibbs ensembles (GGEs), widely studied [1]}, [2]}, [3]}, [4]}. For instance, the initial state could be a profile of temperature, where at each point the system is thermal; but it could be something more general, where many conserved charges are involved. The system is taken to be infinite, although GHD with external force fields, which may constrain the system to a finite length, has also been developed. The fluctuations of the full system may be with respect to any ensemble (micro-canonical, canonical, grand-canonical, and more), as this does not affect the description of local states.
